triqs.utility.bound_and_bisect.bound_and_bisect

triqs.utility.bound_and_bisect.bound_and_bisect(f, x_0, y=0.0, dx=1.0, xtol=0.001, x_name='x', y_name='y', maxiter=1000, verbosity=1)

Solve \(f(x) = y\) for a monotonic function f.

First brackets a sign change of \(F(x) \equiv f(x) - y\) via determine_bounds(), then refines the root with scipy.optimize.bisect().

Parameters:

fcallable

Real-valued, monotonic function of one real argument.

x_0float

Initial guess used to start the outward bracketing search.

yfloat, optional

Target value. Default 0.

dxfloat, optional

Step size used by determine_bounds(). Default 1.0.

xtolfloat, optional

Absolute tolerance on x passed to scipy.optimize.bisect(). Default 1e-3.

x_namestr, optional

Display name for the unknown x, used in the textual report. Default 'x'.

y_namestr, optional

Display name for the function value y, used in the textual report. Default 'y'.

maxiterint, optional

Maximum number of iterations both for the bracketing search and for the bisection step. Default 1000.

verbosityint, optional

Verbosity level. 0 suppresses output; >= 1 prints the bracketing bounds and the final solution to stdout. Default 1.

Returns:

xfloat

Solution of \(f(x) = y\).

fxfloat

Function value \(f(x)\) at the returned solution (should be close to y within the tolerance imposed by xtol).

Raises:

ValueError

Propagated from determine_bounds() if a bracketing interval cannot be found within maxiter steps.